There are many theories abou King Wen's sequence; how it came about and what it signifies. One hypothesis is that each group of 10 see a theme through from its beginning to its culmination.

This seems to be little more than 'seeing patterns in the clouds', as there is no historical evidence for the idea. However, if the pattern sparks an insight or some deeper understanding of the Yijing or the human condition, that is probably reason enough.

Frank Kegan of stars-n-dice.com has put a lot of thought into this, as it seems to fit well with his numerologicial theories concerning the first 10 dots in Pythagoras' number triangle. Look toward the bottom of that page, where he describes the role each of the 64 hexagrams plays in each decade.

His naming and descriptions of the trigrams are informed as much by his somewhat ideosyncratic philosophy as by the Yijing itself. However, it might be interesting to compare the Zhouyi texts for each decade with his interpretation.

The thing with 'cloud-watching' is that it doesn't need special training. More study simply makes for more sophisticated patterns, so anyone can play this game. My take on the 40's decade is on Eric Bryant's blog.

Can you see a pattern along one of the rows of this layout?

This 8 by 8 grid presents the Hou Tian (Later Heaven) hexagram order, traditionally attrubuted to King Wen. It is probably the most familar sequence, established in the original Zhouyi text and followed by every Yi Jing translation.

Compare it with the Xian Tian (Primal Heaven) order shown on the "Early Heaven" layout.

Where the Hou Tian (Later Heaven) sequence of King Wen encapsulates much human meaning, the arrangement above makes the hexagram relationships explicit.

This Xian Tian (Primal Heaven) order has much to commend it. Notice how each row has the same lower trigram and each column comprises all hexagrams that have their upper trigram in common.

This is the oldest form of 'lookup table' or index into the Yi Jing. In each row, only the top three lines change. But they also change in a mathematically consistent way. Notice how line 4 has four yin then four yang across the row. Those groups of four are again split into two yin then two yang. And the top row alternates yin then yang.

Try clicking on one of the hexagrams. You will see that the hexagrams that are immediately related are in the same column or row. This is not a coincidence, but an inevitable result of laying out the hexagrams in this way.

Changing each of the lower trigram lines makes another hexagram in the same column; changing an upper line produces one in the same row. A yang line changes to a hexagram above (left), yin lines go to a hexagram below (right).

The relationship is easy enough to see where only the zhi hexagrams are concerned. But things get more complex when there is more than one change. With the "Colour all" Appearance option selected, clicking on a hexagram produces a pattern with more subtle colouring. Generally, lighter/greyer colours are "farther away": more lines have changed. The yin and yang drift is clearly visible, but this is merely the result of the (binary) numerical ordering: yin lines come before yang.

This layout shows the six-dimensional hypercube (of the "Early Heaven" layout) squashed flat and pulled about so all the hexagrams are visible. It is (probably) the optimal layout in that all the zhi relationships (single line changes) are as close together as possible.

The best way to get to know this layout is to click on lots of hexagrams and watch where its zhi hexagrams appear. Notice that hexagrams with symmetrical lines produce symmetrical patterns. (You may find it useful to choose "Number only" from Appearance and "No tooltip" from Tooltips.)

Notice also that the layout is not confined to mirror images. This layout clearly shows how rotations are an integral part of the inter-hexagram relationships. For example, try 29 then 30, or 64 then 63. Another interesting group are 47/48 and 59/60. Can work out what is happening with 35/26 and 5/6? And what happens as you click up the outer columns from 24 to 23 and from 44 to 43?

This is the layout where the "Colour all" Appearance option comes into its own. For example, click on 12 and see how 10, 13 and 44 are "closer" than 9, 14 and 43! Yet clicking on each of the 3-by-3 grid around 30 (do them in order) demonstrates that the ordering is logical. Compare the zhi pattern with the corresponding 3-by-3 grid around 29.

The Yi-globe comes from The Image of the Cosmos in the I Ching and was developed by József Drasny in 2007. As it is simply the projection of the Yijing's six dimensional binary hypercube onto three dimensions, it is not surprising that a very similar structure was proposed in 1988 by Lothar Teikemeier.

Click on one of the hexagram numbers then rotate the globe by clicking repeatedly on the 10° > button. This gives a 3D view of the "Zhi distances" layout. The 3D effect brings with it some display limitations. For instance, some of the tooltips are inevitably obscured by other hexagrams, and hexagrams that are behind the globe cannot be clicked on.

This is an animation of József's mapping. He goes into considerable depth on his website, and some of the layout choices are informed by his interpretation (see Reconstruction and Analysis). The Yi-globe poles and five circles of latitude correspond to the columns of the Zhi distances layout. For example, the 60°N ring clearly matches the 5th column between 33 and 34.

While József makes a strong case for the Yi-globe being the natural order of the Yijing, I present it here as one of a family of 'natural orders'. The Zhi distances layout is deliberately limited to the mathematical relationships and does not take the Yijing's text and tradition into account. For example, 57 and 58 are placed on the axis as doubled trigrams, where the Zhi distance layout shows 61 and 28 are possibly a better choice if symmetry were the only criterion. It is the consideration of Zhouyi text that recommends the Yi-globe arrangement above the other variants.